Opérateurs pseudodifférentiels et représentations unitaires des groupes de Lie

DOI10.24033/bsmf.2253zbMath0826.22009OpenAlexW2502221238MaRDI QIDQ4698942

Dominique Manchon

Publication date: 12 June 1995

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=BSMF_1995__123_1_117_0

zbMATH Keywords

Fourier transformregularityasymptotic distributionWeyl calculusLie algebraelliptic operatorsunitary irreducible representationsWeyl formulahypoelliptic symbolsanalytic symbol classespseudodifferential operators on Lie groups

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Analysis on real and complex Lie groups (22E30) Pseudodifferential and Fourier integral operators on manifolds (58J40) General properties and structure of real Lie groups (22E15)

Related Items

Beyond the classical Weyl and Colin de Verdière's formulas for Schrödinger operators with polynomial magnetic and electric fields ⋮ Finite difference operators, pseudo-differential calculus and representations of Lie groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Symbolic calculus on nilpotent Lie groups and applications
• Good ideals in the group algebra of a nilpotent Lie group
• Kirillov's character formula for reductive Lie groups
• Weyl symbolic calculus on any Lie group
• Caractères des groupes de Lie
• Asymptotic estimates for spectral functions connected with hypoelliptic differential operators
• Polarization and unitary representations of solvable Lie groups. Appendix by Calvin C. Moore
• Fundamental-series representations of a semisimple Lie group
• Lie Group Convolution Algebras as Deformation Quantizations of Linear Poisson Structures
• UNITARY REPRESENTATIONS OF NILPOTENT LIE GROUPS
• Orbit Method for Nilpotent Lie Groups and Distribution of Eigenvalues
• On the role of the Heisenberg group in harmonic analysis
• ON ASYMPTOTIC DISTRIBUTION OF EIGENVALUES OF PSEUDODIFFERENTIAL OPERATORS IN $ \mathbf R^n$
• ASYMPTOTIC DISTRIBUTION OF EIGENVALUES FOR HYPOELLIPTIC SYSTEMS IN $R^n$
• The weyl calculus of pseudo-differential operators
• Orbites fermées et orbites tempérées
• Caractères des groupes et des algèbres de Lie résolubles
• Formule de Weyl pour les groupes de Lie nilpotents.